Two models for longitudinal item response data

Questionnaires are sometimes administered to the same sample of examinees on more than one occasion. Even when longitudinal data are available, researchers employing item response theory (IRT) often use data only from the first administration for item calibration because there is likely a lack of conditional independence between responses to the same item from the same individual. However, in many longitudinal study designs, the sample size at one occasion is too small for reliable item calibration. Thus, a longitudinal IRT model for use with repeated measures study designs is desirable. This research develops two distinct approaches to longitudinal IRT. One of these models is based on latent class analysis, while the other is based on full-information bi-factor analysis. Both account for the local dependence among items that are administered twice by introducing parameters that describe how the repeated nature of each item affects the response (separately from the effect of the latent trait). The models include parameters that describe the latent trait distribution at the second administration relative to the standardized distribution at time one and the correlation between the latent traits at two time points. The addition of these model components allows item parameters to be calibrated using available data from two occasions